Many-objective flow shop scheduling optimisation with genetic algorithm based on fuzzy sets

To solve many-objective flow-shop scheduling problems (FSP), a genetic algorithm based on the relative entropy of fuzzy sets (REFS_GA) is proposed. A mathematical model of the many-objective FSP is built, which involves four scheduling criterions of FSP. In REFS_GA, the Pareto front is mapped to fuzzy set, and the relational entropy coefficient of fuzzy sets is used to measure the similarity between the fuzzy sets of Pareto solutions and ideal solution. The coefficient is used as the fitness of genetic algorithm (GA) and to guide algorithm evolution. The performance of REFS_GA is evaluated through compared with GA based on g-dominance (gGA), random weight GA (rwGA) and the third version of non-dominated sorting genetic algorithm (NSGA-III). Experiments are carried out with eight DTLZ benchmark functions, six MaF benchmark functions with 4, 7 or 10 objectives, respectively, nine scheduling problems with four objectives and a real-world many-objective FSP. Experimental results show that REFS_GA can solve may-objective benchmark functions and many-objective FSP. The optimisation solution and performance indicators of REFS_GA are better than gGA, rwGA and NSGA-III. It can be concluded that REFS_GA is an effective method to solve many-objective optimisation problems. The main contributions of the work are that a four-objective model of FSP is built and a priori approach based on fuzzy set is proposed to solve many-objective FSP.